daviddoji/Kalman-and-Bayesian-Filters-in-Python
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Merge pull request #403 from AchmadFathoni/AchmadFathoni

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Elaborate how c_0=x_0
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Roger Labbe
2022-05-15 11:01:53 -07:00
committed by GitHub
parent 5655a8ecd5 c45cb6676c
commit dfb23c530f
1 changed files with 7 additions and 0 deletions
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7
07-Kalman-Filter-Math.ipynb
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@@ -294,6 +294,13 @@
"x = e^ce^{kt} \\\\\n",
"x = c_0e^{kt}\\end{gathered}$$\n",
"\n",
"When $t=0$, $x=x_0$. Substitute these to equation above.\n",
"\n",
"$$\\begin{gathered}x_0 = c_0e^{k(0)} \\\\\n",
"x_0 = c_01 \\\\\n",
"x_0 = c_0 \\\\\n",
"x = x_0e^{kt}\\end{gathered}$$\n",
"\n",
"Using similar math, the solution to the first-order equation \n",
"\n",
"$$\\dot{\\mathbf x} = \\mathbf{Ax} ,\\, \\, \\, \\mathbf x(0) = \\mathbf x_0$$\n",